Optimal Assumptions for Synthesis

Controller synthesis is the process of constructing a correct system automatically from its specification. This often requires assumptions about the behaviour of the environment. It is difficult for the designer to identify the assumptions that ensures the existence of a correct controller, and doing so manually can lead to assumptions that are stronger than necessary. As a consequence the generated controllers are suboptimal in terms of generality and robustness. In this work, given a specification, we identify the weakest assumptions that ensures the existence of a controller. We also consider two important classes of assumptions: the ones that can be ensured by the environment and assumptions that speaks only about inputs of the systems. We show that optimal assumptions correspond to strongly winning strategies, admissible strategies and remorsefree strategies respectively. Based on this correspondence, we propose an algorithm for computing optimal assumptions that can be ensured by the environment.Comment: 20 page

Probabilistic causes in Markov chains

The paper studies a probabilistic notion of causes in Markov chains that relies on the counterfactuality principle and the probability-raising property. This notion is motivated by the use of causes for monitoring purposes where the aim is to detect faulty or undesired behaviours before they actually occur. A cause is a set of finite executions of the system after which the probability of the effect exceeds a given threshold. We introduce multiple types of costs that capture the consumption of resources from different perspectives, and study the complexity of computing cost-minimal causes.Comment: Full version of a conference paper at ATVA'21; 26 pages, 9 figure